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2 years ago

Solve for u. 5u-15=30 simplify your answers as much as possible

Mathematics

1 answer:

Musya8 [376]2 years ago

8 0

To solve for u, you add 15 on both sides making it 5u=45, then divide 5 on both sides to got u alone..so making it u=9

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5. Show that the following points are collinear. a) (1, 2), (4, 5), (8,9)

Irina-Kira [14]

Label the points A,B,C

A = (1,2)
B = (4,5)
C = (8,9)

Let's find the distance from A to B, aka find the length of segment AB.

We use the distance formula.

$A = (x_1,y_1) = (1,2) \text{ and } B = (x_2, y_2) = (4,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (2-5)^2}\\\\d = \sqrt{(-3)^2 + (-3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d = \sqrt{9*2}\\\\d = \sqrt{9}*\sqrt{2}\\\\d = 3\sqrt{2}\\\\$

Segment AB is exactly $3\sqrt{2}$ units long.

Now let's find the distance from B to C

$B = (x_1,y_1) = (4,5) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-8)^2 + (5-9)^2}\\\\d = \sqrt{(-4)^2 + (-4)^2}\\\\d = \sqrt{16 + 16}\\\\d = \sqrt{32}\\\\d = \sqrt{16*2}\\\\d = \sqrt{16}*\sqrt{2}\\\\d = 4\sqrt{2}\\\\$

Segment BC is exactly $4\sqrt{2}$ units long.

Adding these segments gives

$AB+BC = 3\sqrt{2}+4\sqrt{2} = 7\sqrt{2}$

----------------------

Now if A,B,C are collinear then AB+BC should get the length of AC.

AB+BC = AC

Let's calculate the distance from A to C

$A = (x_1,y_1) = (1,2) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (2-9)^2}\\\\d = \sqrt{(-7)^2 + (-7)^2}\\\\d = \sqrt{49 + 49}\\\\d = \sqrt{98}\\\\d = \sqrt{49*2}\\\\d = \sqrt{49}*\sqrt{2}\\\\d = 7\sqrt{2}\\\\$

AC is exactly $7\sqrt{2}$ units long.

Therefore, we've shown that AB+BC = AC is a true equation.

This proves that A,B,C are collinear.

For more information, check out the segment addition postulate.

7 0

2 years ago

For 5-9, use the diagram below to classify each of the angles.

NARA [144]

Oh yeah lol I just don’t think can

4 0

2 years ago

the height of mont blanc is 4810 m correct to the nearest 10 meters. what is its least possible height

SSSSS [86.1K]

Answer:

4800m

Step-by-step explanation:

"correct to the nearest 10 meters" means that the height can vary ± 10 meters.

4810 m ± 10 m = 4800 to 4820

4800 is the least possible height.

7 0

2 years ago

Solve over the set of real numbers for the equation below x-2=√2x-1

Anon25 [30]

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

<h3>What is the solution of the equation?</h3>

The solution of the equation means the value of the unknown or variable.

The equation is given below.

x – 2 = √(2x – 1)

Square on both side, then we have

(x – 2)² = 2x – 1

x² – 4x + 4 = 2x – 1

x² – 6x + 5 = 0

x² – 5x – x + 5 = 0

x(x – 5) – 1(x – 5) = 0

(x – 5)(x – 1) = 0

x = 1, 5

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

More about the solution of the equation link is given below.

brainly.com/question/545403

#SPJ1

6 0

1 year ago

Can someone please explain to me how to solve this equation?

Nikolay [14]

Answer:

first of all erase what u have written

Step-by-step explanation:

25-3x-5=2x+16+x
20-6x=16
6x=4
x=2/3

6 0

3 years ago